※ 引述《ilovecurl (ilovecurl)》之铭言： : http://www.lib.nccu.edu.tw/exam/transfer/math/index.htm : 这个是政大应数考古题的网址 : 我要问的是92年微积分(一)的第3,6,7题 : 题目如下,看不清楚的可以去上面的网址看 : 3.the series : ∞ cos(n^p) ∞ (lnn)^β cos(n^p) : Σ ------------ and Σ -------------------- : n=2 n(lnn)^α n=2 n^α : converge for every α>1,β>=1 and p>=1. : 6.the following series is a rearrangement of the alternating harmonic : series in which there appear alternately three positive terms followed : by two negative terms : 1 1 1 1 1 1 1 1 1 : 1 + --- + --- - --- - --- + --- + --- + ---- - --- - --- +++--... : 3 5 2 4 7 9 11 6 8 : show that this series converges and has sum ln(√6). : 7.for the sequence of functions f_n(x) = (x^2-1)^n. : (3) : define g_n(x) = f_n (x), n>=1. g_0(x) = 1. : then prove or disprove g_n(x) converges uniformly in [0,√2]. 这个第七题我会了,不过上面的两题还是想不出来,有没有好心的大大po一下详解啊 另外同样是这张的第4,5题问的题目,我不是很肯定他的意思 A farmer has 1000 feet of fence and wants to build a rectangular enclosure along a straight wall.If the side along the wall needs no fence. 4.Find the dimensions that make the enclosure as large as possible. 5.Find the maximum area. 以下是我所理解的题意 wall ------------------- x | | x ------------------- 1000-2x 上面的x是我自己假设的,然後求出最大的长方形面积和此时的长宽尺寸 不知道4.5题是不是这个意思,因为如果是,好像太简单,感觉很奇怪,请各位帮个忙吧! --

※ 发信站: 批踢踢实业坊(ptt.cc) ◆ From: 59.113.184.218